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Distributions: separate sample histogram test for continuous and discrete distributions

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Christoph Ruegg 13 years ago
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44b0b12db3
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bca96c569d
2 changed files with 70 additions and 38 deletions
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  1. 100
      src/UnitTests/DistributionTests/CommonDistributionTests.cs
  2. 8
      src/UnitTests/DistributionTests/Multivariate/NormalGammaTests.cs

100
src/UnitTests/DistributionTests/CommonDistributionTests.cs
View File

@ -59,11 +59,11 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
new Categorical(new[] { 0.7, 0.3 }),
//new ConwayMaxwellPoisson(0.2, 0.4),
new DiscreteUniform(1, 10),
//new Geometric(0.1),
//new Geometric(0.2),
new Hypergeometric(20, 3, 5),
//new NegativeBinomial(4, 0.6),
//new Poisson(0.4),
new Zipf(0.6, 10),
new Zipf(3.0, 10),
};
readonly List<IContinuousDistribution> _continuousDistributions =
@ -134,55 +134,55 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
}
}
/// <summary>
/// Test the method which samples only one variable at a time.
/// </summary>
[Test]
public void SampleFollowsCorrectDistribution()
public void DiscreteSampleIsDistributedCorrectly()
{
foreach (var dd in _discreteDistributions)
foreach (var dist in _discreteDistributions)
{
dd.RandomSource = new SystemRandomSource(1, false);
var samples = new double[NumberOfTestSamples];
dist.RandomSource = new SystemRandomSource(1, false);
var samples = new int[NumberOfTestSamples];
for (var i = 0; i < NumberOfTestSamples; i++)
{
samples[i] = dd.Sample();
samples[i] = dist.Sample();
}
DiscreteVapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, dist);
}
}
VapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, dd);
[Test]
public void DiscreteSampleSequenceIsDistributedCorrectly()
{
foreach (var dist in _discreteDistributions)
{
dist.RandomSource = new SystemRandomSource(1, false);
var samples = dist.Samples().Take(NumberOfTestSamples).ToArray();
DiscreteVapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, dist);
}
}
foreach (var cd in _continuousDistributions)
[Test]
public void ContinuousSampleIsDistributedCorrectly()
{
foreach (var dist in _continuousDistributions)
{
cd.RandomSource = new SystemRandomSource(1, false);
dist.RandomSource = new SystemRandomSource(1, false);
var samples = new double[NumberOfTestSamples];
for (var i = 0; i < NumberOfTestSamples; i++)
{
samples[i] = cd.Sample();
samples[i] = dist.Sample();
}
VapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, cd);
ContinuousVapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, dist);
}
}
/// <summary>
/// Test the method which samples a sequence of variables.
/// </summary>
[Test]
public void SamplesFollowsCorrectDistribution()
public void ContinuousSampleSequenceIsDistributedCorrectly()
{
foreach (var dd in _discreteDistributions)
foreach (var dist in _continuousDistributions)
{
dd.RandomSource = new SystemRandomSource(1, false);
var samples = dd.Samples().Select(x => (double)x).Take(NumberOfTestSamples).ToArray();
VapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, dd);
}
foreach (var cd in _continuousDistributions)
{
cd.RandomSource = new SystemRandomSource(1, false);
var samples = cd.Samples().Take(NumberOfTestSamples).ToArray();
VapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, cd);
dist.RandomSource = new SystemRandomSource(1, false);
var samples = dist.Samples().Take(NumberOfTestSamples).ToArray();
ContinuousVapnikChervonenkisTest(ErrorTolerance, ErrorProbability, samples, dist);
}
}
@ -193,10 +193,10 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void VapnikChervonenkisTest(double epsilon, double delta, double[] s, IUnivariateDistribution dist)
public static void ContinuousVapnikChervonenkisTest(double epsilon, double delta, double[] s, IContinuousDistribution dist)
{
// Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
// For intervals on the real line the VC-dimension is 2.
Assert.Greater(s.Length, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
@ -205,7 +205,39 @@ namespace MathNet.Numerics.UnitTests.DistributionTests
for (var i = 0; i < NumberOfHistogramBuckets; i++)
{
var p = dist.CumulativeDistribution(histogram[i].UpperBound) - dist.CumulativeDistribution(histogram[i].LowerBound);
var pe = histogram[i].Count / s.Length;
var pe = histogram[i].Count/(double)s.Length;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}
/// <summary>
/// Vapnik Chervonenkis test.
/// </summary>
/// <param name="epsilon">The error we are willing to tolerate.</param>
/// <param name="delta">The error probability we are willing to tolerate.</param>
/// <param name="s">The samples to use for testing.</param>
/// <param name="dist">The distribution we are testing.</param>
public static void DiscreteVapnikChervonenkisTest(double epsilon, double delta, int[] s, IDiscreteDistribution dist)
{
// Using VC-dimension, we can bound the probability of making an error when estimating empirical probability
// distributions. We are using Theorem 2.41 in "All Of Nonparametric Statistics".
// http://books.google.com/books?id=MRFlzQfRg7UC&lpg=PP1&dq=all%20of%20nonparametric%20statistics&pg=PA22#v=onepage&q=%22shatter%20coe%EF%AC%83cients%20do%20not%22&f=false .</para>
// For intervals on the real line the VC-dimension is 2.
Assert.Greater(s.Length, Math.Ceiling(32.0 * Math.Log(16.0 / delta) / epsilon / epsilon));
var min = s.Min();
var max = s.Max();
var histogram = new int[max - min + 1];
for (int i = 0; i < s.Length; i++)
{
histogram[s[i] - min]++;
}
for (int i = 0; i < histogram.Length; i++)
{
var p = dist.CumulativeDistribution(i + min) - dist.CumulativeDistribution(i + min - 1.0);
var pe = histogram[i]/(double)s.Length;
Assert.Less(Math.Abs(p - pe), epsilon, dist.ToString());
}
}

8
src/UnitTests/DistributionTests/Multivariate/NormalGammaTests.cs
View File

@ -349,14 +349,14 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
var precMarginal = cd.PrecisionMarginal();
// Check the precision distribution.
CommonDistributionTests.VapnikChervonenkisTest(
CommonDistributionTests.ContinuousVapnikChervonenkisTest(
CommonDistributionTests.ErrorTolerance,
CommonDistributionTests.ErrorProbability,
precs,
precMarginal);
// Check the mean distribution.
CommonDistributionTests.VapnikChervonenkisTest(
CommonDistributionTests.ContinuousVapnikChervonenkisTest(
CommonDistributionTests.ErrorTolerance,
CommonDistributionTests.ErrorProbability,
means,
@ -381,14 +381,14 @@ namespace MathNet.Numerics.UnitTests.DistributionTests.Multivariate
var precMarginal = cd.PrecisionMarginal();
// Check the precision distribution.
CommonDistributionTests.VapnikChervonenkisTest(
CommonDistributionTests.ContinuousVapnikChervonenkisTest(
CommonDistributionTests.ErrorTolerance,
CommonDistributionTests.ErrorProbability,
precs,
precMarginal);
// Check the mean distribution.
CommonDistributionTests.VapnikChervonenkisTest(
CommonDistributionTests.ContinuousVapnikChervonenkisTest(
CommonDistributionTests.ErrorTolerance,
CommonDistributionTests.ErrorProbability,
means,

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